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A New Genetic Algorithm Method for Optimal

Coordination of Overcurrent Relays in a Mixed

Protection Scheme with Distance RelaysHossein.Askarian.Abyaneha

[email protected]

Somayeh.Sadat.Hashemi.Kamangara

MSc. [email protected]

Farzad.RazaviAssistant Professor

[email protected]

Reza.Mohammadi.Chabanlooa

PhD. [email protected]

AbstractSeveral optimal coordination of overcurrent relayshave been done in the past by using linear programming such assimplex, two-phase simplex and dual simplex and also intelligentoptimization techniques such as genetic algorithm (GA)techniques. In this paper, a powerful optimal coordinationmethod based on GA is introduced. The objective function (OF)is developed in a way that in addition to coordination ofovercurrent relays, the coordination of overcurrent and distancerelays is achieved. In other words, the novelty of the paper is themodification of the existing objective function of GA, by addinga new term to OF to fulfill the coordination of both overcurrentand distance relays. The method is applied to a power networksystem and from the obtained results it is revealed that the newmethod is efficient and accurate.

Index TermsOvercurrent Relay, Distance Relay, OptimalCoordination, Genetic Algorithm.

I. INTRODUCTIONOvercurrent (OC) and distance relays are commonly used

for transmission and subtransmission protection systems [1].

To consider comprehensive coordination, a distance relay

with a distance one, an overcurrent relay with an overcurrentone and finally a distance relay with an overcurrent one when

one of them is considered to be the main relay and the other isthe backup, must be coordinated.

When both considered main and backup (M/B) relays aredistance types, the impedances of the three zones of relays are

calculated considering all conditions of an interconnectednetwork such as connecting and disconnecting of generatorsand lines [2].

For overcurrent relays the optimal coordination has been performed using linear programming techniques, includingsimplex [3], two-phase simplex [4] and dual simplex [5]

methods. In reference [6] also, optimal solution is made by

constraints only. The disadvantage of the above optimizationtechniques is that they are based on an initial guess and may be trapped in the local minimum values [7]. Intelligent

optimization techniques such as genetic algorithm (GA) canadjust the setting of the relays without the mentioneddifficulties.

aDepartment of Electrical Engineering, Amirkabir University of Technology,

Tehran, Iran.b

Department of Electrical Engineering, Tafresh University, Tafresh, Iran.

In these methods the constraints are included in objectivefunction [7]. The optimal coordination in reference [8] has

been done by a method based on GA and in reference [9] byan evolutionary algorithm. These methods have twoproblems. One of them is miscoordination and the other is not

having the solution for relays with both discrete andcontinuous time setting multipliers (TSMs). In reference [7]the mentioned problems have been solved.

In the cases that the distance relay is considered to be mainand the overcurrent one is the backup relay, it is necessary tofind the critical fault locations. The critical fault locations arethe positions when faults considers on those points, the

discrimination time (t) between the backup and main relaysis minimum. The coordination is made based on theconstraints derived from the values of t for critical fault

locations.In references [1] & [10] coordination of overcurrent,

distance and circuit breaker failure (CBF) relays has beendone using linear programming techniques.

In this paper a new optimal coordination method based onGA is introduced. The objective function (OF) is developed

by adding a new term that is the constraint related to thecoordination of the distance and overcurrent relays when afault occurs at the critical locations.

II. REVIEW OF RECENTLY DEVELOPED GA FOROPTIMAL OCRELAY COORDINATION

GA like all other optimization methods needs initial values

which are chosen randomly. TSMs of relays are the unknown

quantities in the optimization problem. Therefore, the TSMs

in respect to the number of relays are considered as the

genomes of the chromosomes in GA. In other words, some

TSMs sets, i.e. (TSM1, TSM2, TSM3, , TSMn), (TSM1,

TSM2, TSM3, , TSMn), belonging to relay set (R1, R2,R3, , Rn) are initially randomly selected. The number of

TSMs sets is referred as the population size. Then, after each

iteration, the new TSMs sets belong to relays R1 to Rn are

given to the algorithm. The process is terminated when the

number of iterations becomes equal to the generation size [7].

To evaluate the goodness of each chromosome, it is

essential to define an OF. The purpose of optimization is to

minimize the OF. The chromosomes are evaluated regarding

the OF and the chromosomes which have more effectiveness

will be used for producing new generation of chromosomes.


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Mutation in each iteration will cause the algorithm not to trap

in local minimums.

After a fixed number of generations, the process will be

terminated. Increasing the number of generations will lead to

the better solutions and on the other hand, will increase the

run time. The required number of generation varies from

system to system depending on the system complexity and

the size of population [7].

III. PROBLEM STATEMENTAs mentioned in section , relay coordination must be done

for the cases below:

1) Coordination of overcurrent relays with overcurrentones.

2) Coordination of distance relays with distance ones.3) Coordination of distance relays with overcurrent ones.As mentioned in section II, the first one has been made in

the frame of GA. In this paper, it is necessary to be done the

optimal coordination in a way that all three cases above are

satisfied. For the third case it is assumed that the distancerelay is the main relay and the overcurrent relay is the

backup. This assumption is a routine protection scheme in

power networks. In interconnected networks, an overcurrent

relay can be the backup of some other distance relays.

Therefore, TSMs of all overcurrent relays and the operating

time the second zone of all distance relays must be

determined for critical conditions. The critical condition is

defined and shown in Fig. 1. An overcurrent relay is located

at B and a distance one at M. The overcurrent relay is the

backup of distance relay. When a fault occurs at F, the

discrimination time between the operating time of overcurrent

relay and that of the distance one is minimum. Therefore, theexpression below must be appointed at the critical fault

location, F.

( ) CTItFt 2Zb > (1)

Where ( )Ftb is the operating time of overcurrent relay atF, 2Zt is the operating time of the second zone of the distance

relay and CTI is the coordination time interval.

As mentioned above, coordination between overcurrent and

distance relays must be made by adding a new constraint to

OF in GA. The details of this method are described in section

IV.

IV.NEW METHODIn the new method, the OF is formulated as:

( )

( )2P

1kkmbDISOCkmbDISOC3

P

1k

2

kmbkmb2

N

1i

2i1

2

2

22

1

1

11

tt

tt

tFO

=

=

=

+

+

= )(.

(2)

Where 321 ,, are the weighting factors, i is the number

of overcurrent relays that changes from 1 to N, 1k is thenumber of main and backup overcurrent relays that changes

from 1 to 1P , 2k is the number of mai distance and backup

overcurrent relays changing from 1 to 2P , 1kmbt is the

discrimination time between the main and backup overcurrent

relays.2kmbDISOC

t is the discrimination time between the

main distance and backup overcurrent relays which isobtained from the equation below:

CTIttt222 kmDISkbOCkmbDISOC= (3)

Where 2kbOCt is the operating time of backup overcurrent

relay for the fault at the end of the first zone of main distance

relay(critical fault locations),2kmDIS

t is the operating time of

the second zone of main distance relay and CTI is the

coordination time interval that is equal to 0.3(sec).Two first terms of (2) are the same as the OF in [7]. The

third term is added to OF to fulfill the requirement ofovercurrent and distance relays. To describe the role of this

new term, consider2kmbDISOC

t to be positive, then the

relative term is zero, however if2kmbDISOC

t is negative the

mentioned term will be2kmbDISOC

3 t2 and obviously for

positive values of 3 the new term will have great values.

Then, based on a concept of the evaluation and selection parts

of GA, those values that have more optimal OF values (lessvalue) in the chromosomes, are granted more opportunities toselect for the next iteration.

The flowchart of new method is shown in Fig. 2. At first,after entering the network data, the impedances of the first,second and the third zones of distance relays are calculated.Then, the short circuit currents for the faults exactly close tothe circuit breaker (CB) of the main overcurrent relays andfor the faults at the end of the first zone of main distance

Fig. 1. Critical fault location in coordination between overcurrent anddistance relays


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relays( critical fault locations) are calculated. After that, GA

will start. The operating time of the second and third zones ofdistance relays are selected respectively 0.3(sec) and 0.6(sec)

and1kmbi

tt , and2kmbDISOC

t are calculated using short

circuit currents. The other steps of GA are described in

section II and in [7].

V. TEST CASEThe new method proposed in this paper, is applied to a

power network shown in Fig. 3. This network consists of 6

buses, 7 lines, 2 transformers and 2 generators. The

information data of the network is given in Tables I, II and

III. R (pu) and X (pu) are based on 100 MVA and 150 kV. It

is assumed that all the lines are protected by both overcurrent

and distance relays. All distance relays have moho

characteristic.

It should be noted that for finding the overcurrent relays

operating times, a more common formula for approximatingthe relay characteristic is used [7, 11]:

( ) ( ) ( )

+

+

+

+=3

3

2

210

1M

a

1M

a

1M

aa

TSM

t (4)

Where M is the ratio of short circuit current ( scI ) to the

pickup current ( bI ) of relay ( bsc IIM /= ), t is the relay

operating time and ,...,,, 3210 aaaa are the scalar quantities

and for overcurrent relays with normal inverse characteristicsthat are used in this paper, these quantities are [7]:

0003199010a03644650a

461290a579228a987721a

4

3

2

1

0

..

...

===

==

(5)

It is also assumed that TSMs of the relays are discrete and

TSMs vary from 0 to 1 in steps of 0.05.

The control parameters of GA are listed in Table IV. To

compose OF, the values of 321 ,, are mentioned asbelow:

1001001 321 === ,, (6)

TABLE ILINESINFORMATION OF SAMPLENETWORK

Line R (pu) X (pu) V (kV)

1 0.0018 0.0222 150

2 0.0018 0.0222 150

3 0.0018 0.02 150

4 0.0022 0.02 150

5 0.0022 0.02 150

6 0.0018 0.02 150

7 0.0022 0.0222 150

TABLE IIGENERATORSINFORMATION OF SAMPLENETWORK

GeneratorX (pu) V (kV)

0.1 10

21 kmbDISOCkmbittt ,,

( )

( )2

P

1k

kmbDISOCkmbDISOC3

P

1k

2

kmbkmb2

N

1i

2

i1

2

2

22

1

1

11

tt

tt

tOF

=

=

=

+

+= )(

Evaluation

Fig. 2. Flowchart of new method

Fig. 3. Sample network


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TABLE IIITRANSFORMERSINFORMATION OF SAMPLENETWORK

TransformerX (pu)

0.02666

By applying the GA with selected values, the output results

for TSMs are obtained. These TSMs are given in Table V.

The operating time of the second and third zones of distance

relays are selected respectively 0.3(sec) and 0.6(sec).

From the second column of Table V, it can be seen that the

values of TSMs are small and they are in valid range, i.e.

between 0.05 and 1.Discrimination time between M/B overcurrent relays and

discrimination time between the main distance and backup

overcurrent relays are given in Table VI. All1kmb

t (sec) and

2kmbDISOCt (sec) values are positive and most of them are

small. That means, the relay settings are accurate, fit and havenot any miscoordination.

TABLE IVCONTROL PARAMETERS OF GA

GA Parameters Value

Number of Generations 2500

Size of population 100

Initial Population Random

Mutation 1

TABLE VTSMS OF OVERCURRENT RELAYS

Relay

NumbersTSM

1 0.1

2 0.2

3 0.15

4 0.05

5 0.05

6 0.2

7 0.1

8 0.15

9 0.05

10 0.1

11 0.15

12 0.25

13 0.05

14 0.1

TABLE VIDISCRIMINATION TIMES OF M/BRELAYS

Main

Relay

Backup

Relay(sec)

1kmbt

(sec)2kmbDISOC

t14 1 0.6527 0.0000

3 2 0.0024 0.2676

4 3 0.1082 0.0016

5 4 0.1000 0.0000

6 5 0.0000 0.0000

7 5 0.0000 0.0000

1 6 0.0036 0.2122

2 7 0.1702 0.1749

8 7 0.2790 0.0024

13 8 0.0030 0.0559

8 9 0.0000 0.0000

14 9 0.0000 0.0000

9 10 0.0028 0.0000

10 11 0.0039 0.0175

11 12 0.0021 0.2044

7 13 0.0000 0.0000

6 14 0.2887 0.0000

12 14 0.1561 0.2203

2 1 0.1387 0.0000

12 13 0.0110 0.0000

VI. CONCLUSIONA new computer program for distance and overcurrent

relay coordination based on GA has been developed. In theproposed method, the OF has been modified by adding a new

term which presents the constraint for distance and

overcurrent relay coordination. The computer program has

been tested on a power system network. From the obtained

results, it has been shown that the new method is successful

and accurate.

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